Question

Which of the following correctly demonstrates the Associative Property of Addition?(1 point) Responses (x+y)+z+r=x+(y+z)+r left parenthesis x plus y right parenthesis plus z plus r equals x plus left parenthesis y plus z right parenthesis plus r m⋅(x⋅y)=(m⋅x)⋅y m times left parenthesis x times y right parenthesis equals left parenthesis m times x right parenthesis times y x⋅(y+z)=(x⋅y)+z x times left parenthesis y plus z right parenthesis equals left parenthesis x times y right parenthesis plus z y−(x+1)=(y−x)+1 y minus left parenthesis x plus 1 right parenthesis equals left parenthesis y minus x right parenthesis plus 1

Answer 1

The Associative Property of Addition states that when you add three or more numbers, the way in which the numbers are grouped does not change the sum. It can be expressed as:

\[(a + b) + c = a + (b + c)\]

From the options you've provided, the statement that correctly demonstrates the Associative Property of Addition is:

\[(x + y) + z + r = x + (y + z) + r\]

This clearly shows that the grouping of \(x\), \(y\), and \(z\) does not affect the sum when added to \(r\).

So the correct answer is:

\((x+y)+z+r=x+(y+z)+r\)